Why don't effectors effect effectors?
You can work around this by parenting force-field empties to the rigid bodies instead of making the rigid-bodies effectors themselves:


Add the force field: ShiftA>Force field > Force.
Parent it to your rigid-body sphere. Select the force-field, then the sphere and press CtrlP> Object.



It is important that the force-field has the same rotation and location as the sphere.


The force-fields will not have any affect on the sphere they are parented to, as the center of mass of the sphere is in the same place as the center of the force-field. They will affect the other spheres though.

Example animation (click for html5 version):



Example .blend